Information Theoretic Regret Bounds for Online Nonlinear Control
This addresses the challenge of online nonlinear control with unknown dynamics for applications in robotics and autonomous systems, representing a significant theoretical advance rather than an incremental improvement.
The paper tackles the problem of sequential control in unknown nonlinear dynamical systems by modeling dynamics as an unknown function in a Reproducing Kernel Hilbert Space, achieving a near-optimal O(sqrt(T)) regret bound against the optimal controller with no explicit dependence on system dimension.
This work studies the problem of sequential control in an unknown, nonlinear dynamical system, where we model the underlying system dynamics as an unknown function in a known Reproducing Kernel Hilbert Space. This framework yields a general setting that permits discrete and continuous control inputs as well as non-smooth, non-differentiable dynamics. Our main result, the Lower Confidence-based Continuous Control ($LC^3$) algorithm, enjoys a near-optimal $O(\sqrt{T})$ regret bound against the optimal controller in episodic settings, where $T$ is the number of episodes. The bound has no explicit dependence on dimension of the system dynamics, which could be infinite, but instead only depends on information theoretic quantities. We empirically show its application to a number of nonlinear control tasks and demonstrate the benefit of exploration for learning model dynamics.